Decentralized Stochastic Optimal Control for a Swarm of Micro Aerial Vehicles

Abstract

In this work, we model a multi-robot formation planning and control task as an optimization problem, which we solve on-line and in a decentralized manner using the Stochastic Optimal Control (SOC) framework. Typically, the solution of a SOC problem requires solving the Hamilton-Jacobi-Bellman (HJB) equation for all system states and controls. However, this operation becomes intractable when high-dimensional systems are used. In recent years, advances on a certain type of SOC problem, which can be efficiently solved by sampling from a diffusion process have been presented and are better known as path integral (PI) control. We build upon this theory and implement a decentralized formulation of the PI algorithm to compute the optimal controls of real Micro Aerial Vehicles (MAVs) flying in formation using solely on-board computational resources. One challenging aspect of the PI control method is the efficient sampling of useful trajectories. It is not clear how to guide the samples towards the optimal states. To this end, we propose a probe enhanced importance sampling (PEIS) method which performs a coarse exploration of the state space with the objective of identifying an optimal guiding trajectory around which the samples are taken. The feasibility of the proposed method is shown by means of simulation and real-hardware experiments with up to four MAVs in an indoor environment.